The spectral/hp element method provides an efficient approach for implicit Large-Eddy Simulations (iLES) of incompressible flows. However, the simulation of highly-resolved incompressible flow on industrial geometries is often limited by computational resources. This is particularly severe in advection-dominated flows where high Reynolds numbers cause strong stability restrictions on the maximum-allowable time step size and, thus, significantly increase the time-to-solution. This issue renders algorithms like velocity-correction Schemes inefficient due to their explicit treatment of the advection terms. In an effort to reduce computational costs for industrial geometries, we investigate a velocity-correction scheme with linearly-implicit treatment of the advection terms based on the work of [6, 19]. We consider an extension of this work to determine the possible efficiency gain in quasi-3D simulations where one resolves the three-dimensional nature of the flow whilst reducing computational cost through the assumption of a homogeneous/spectral dimension. This algorithm gains efficiency by treating only the mean-mode of each velocity component implicitly while treating higher-frequency modes explicitly. Thus, the algorithm stabilises the computation by making the bulk of the energy implicit. Initial results show that the scheme is capable of a strong improvement in stability. The present paper present our progress along with numerical tests.